Extending stochastic resonance for neuron models to general Levy noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Levy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general Levy noise models. We achieve this by showing that �¿large jump�¿ discontinuities in the noise can be controlled so as to allow the stochastic model to tend to a deterministic one as the noise dissipates to zero. SR then follows by a �¿forbidden intervals�¿ theorem as in Patel and Kosko's paper

Ornstein-Uhlenbeck Process via Conflated Drive of Brownian Motion and Lévy Process and its Application

Non-linear time series and linear models were not designed to detect probabilistic process that are depict by velocity and drift associated to returns the way Ornstein-Uhlenbeck stochastic process describes diffusion and velocity associated to series or waves influenced by Brownian motion or Lévy process.  In this research, Brownian motion and Lévy process were conflated as driving force for Ornstein-Uhlenbeck process with its solution applied to Naira-Dollar exchange rates from 2009-2019.The drift and diffusion estimates for the Ornstein-Uhlenbeck process driven by Brownian motion and Lévy process are realization of AR (1) with 2.991 and 0.1672 respectively. The AR(1) realization for the Ornstein-Uhlenbeck process was stationary with estimate  that lies outside the unit circle. The AIC, BIC, RMSE, and MSE for the Ornstein-Uhlenbeck process were estimated to be 483.7572, 483.4782, 0.00101, and 8.395 respectively, compare to estimates of the same indexes for AR (1) of 767.5, 634.09, 0.3819, and 23.48. The criterion via the residuals from the Ornstein-Uhlenbeck process was smaller, which connotes that the errors approximated in using drift, Brownian motion and to estimate  is relatively small via the Ornstein-Uhlenbeck process. Keywords: Brownian motion; Drift; Diffusion; Lévy process; Ornstein-Uhlenbeck Process DOI: 10.7176/MTM/11-3-02 Publication date:May 31st 202

Overreaction and Multiple Tail Dependence at the High-frequency Level — The Copula Rose

This paper applies a non- and a semiparametric copula-based approach to analyze the first-order autocorrelation of returns in high frequency financial time series. Using the EUREX D3047 tick data from the German stock index, it can be shown that the temporal dependence structure of price movements is not always negatively correlated as assumed in the stylized facts in the finance literature. Depending on the sampling frequency, the estimated copulas exhibit some kind of overreaction phenomena and multiple tail dependence, revealing patterns similar to the compass rose.High Frequency Data, Non- and Semiparametric Copulas, Overreaction, Tail Dependence, Compass Rose

A Slab in the Face: Building Quality and Neighborhood Effects

The quality of newly constructed single-family houses is usually homogeneous in and heterogeneous between neighborhoods. Such quality-clustering will be caused by the variation of natural amenities throughout a suburban area. Clustering will be enforced if the quality of neighboring buildings increases the value of newly constructed ones. To disentangle the natural amenity eect and the neighborhood eect, we use data from Berlin and exploit that the endogenous eect was weakened during the socialist period. Our results show that the exogenous variation caused by buildings constructed during this period still causes lower quality new buildings in the East of the city.housing supply, housing externality, natural experiment

Dynamic asset allocation using option implied distributions in an exponentially tempered stable Lévy market

Mestrado em Mathematical FinanceEste artigo explora o problema do portfólio ideal usando distribuições implícitas na opção quando o processo de preço subjacente é assumido como sendo conduzido por um processo exponencial de Levy. Em particular, a aplicação é levada a cabo usando um processo de difusão de salto Estável Exponencialmente Temperado como o componente martingale do preço das acções de log, e as preferências do investidor são assumidas sujeitas a uma função de utilidade CRRA. Densidades de um mês neutras ao risco são extraídas dos preços das opções usando um método de precificação por transformação e são subsequentemente transformadas na densidade ajustada ao risco ou no mundo real por meio de um modelo preservando a entropia mínima que mantém a parametrização do processo Levy. Um resultado de controle otimizado estocástico é então usado para construir um portfólio que consiste em um ativo de risco e sem risco, que é reequilibrado mensalmente. Descobriu-se que os portfólios formados usando as expectativas implícitas na opção sob a hipótese de mercado Levy, que são flexíveis o suficiente para capturar os momentos mais altos da distribuição implícita, são muito mais robustos aos riscos de cauda esquerda e oferecem melhorias estatisticamente significativas ao desempenho ajustado ao risco quando a aversão ao risco do investidor é baixa, porém isso diminui à medida que aumenta a aversão ao risco.This paper explores the optimal portfolio problem using option-implied distributions when the underlying price process is assumed to be driven by an exponential Levy process. In particular, the application is carried out using an Exponentially Tempered Stable jump-diffusion process as the martingale component of the log stock price, and the investor's preferences are assumed subject to a CRRA utility function. One month risk-neutral densities are extracted from option prices by using a transform pricing method and are subsequently transformed to the risk-adjusted, or real-world density via a model preserving minimal entropy transform which importantly maintains the parameterization of the Levy process. A stochastic optimal control result is then used to construct a portfolio consisting of a risky and risk-free asset which is rebalanced on a monthly basis. It is found that the portfolios formed using option-implied expectations under the Levy market assumption, which are flexible enough to capture the higher moments of the implied distribution, are far more robust to left-tail market risks and offer statistically significant improvements to risk-adjusted performance when investor risk aversion is low, however this diminishes as risk aversion increases.info:eu-repo/semantics/publishedVersio

A Jump Ornstein-Uhlenbeck Bridge Based on Energy-optimal Control and Its Self-exciting Extension

We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.Comment: This is a revised versio

Stock jumps: Analyzing traditional and behavioral perspectives

Our aim is to define the concept of stock jumps from a practitioner's perspective and to give an insightful overview of the topic. We provide different technical and practical definitions from distinct points of view: mathematical, risk managerial, trading and investing. We verify the robustness of some common stylised facts for three major stock indices, and we derive an approximated jumps distribution. We finally provide some innovative insights from a behavioral perspective, and how to account for behavioral biases in this context